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pernicious n.  and  repunit

First numbers that belong to both sets:

7, 13, 21, 31, 40, 73, 91, 121, 127, 133, 157, 211, 241, 259, 273, 307, 341, 364, 381, 400, 421, 463, 601, 651, 757, 781, 820, 871, 1057, 1123, 1261, 1483, 1555, 1561, 1807, 1893, 2047, 2071, 2257, 2353, 2380, 2653, 2801, 2955, 3193, 3280, 3661, 3907, 4033, 4161, 4291, 4557, 4681, 5220, 5257, 5403, 5461, 6163, 6175, 7240, 8191, 8557, 8931, 9313, 9331, 9841, 10921, 11557, 11773, 12433, 12657, 12883, 13341, 13807, 14425, 16513, 16771, 17293, 19461, 19531, 22053, 23563, 23871, 24493, 25260, 25441, 30451, 30784, 30801, 31863, 32943, 34783, 35157, 35911, 36673, 37057, 37060, 40201, 41007, 41413, 44136, 44733, 45157, 46011, 47989, 49507, 50401, 52213, 54523, 54991, 55933, 57361, 58807, 59293, 60763, 62751, 65641, 65793, 66307, 67341, 69905, 72631, 73713, 74257, 74803, 78121, 79807, 80373, 81400, 81511, 82657, 84973, 88507, 93196, 93943, 95791, 97656, 101443, 105951, 109231, 110557, 111223, 112561, 114583, 116623, 118681, 120063, 121453, 122151, 122851, 127807, 129241, 131071, 131407, 132133, 135793, 138757, 143365, 147841, 154843, 156421, 159601, 161203, 162007, 163621, 166057, 172641, 178809, 180201, 183613, 188500, 188791, 189661, 191407, 194041, 200257, 201153, 204205, 205663, 206571, 210223, 212061, 216691, 220431, 226101, 227053, 232807, 234741, 240591, 242235, 242557, 243543, 245521, 247507, 251503, 253513, 255531, 257557, 259591, 262657, 263683, 265741, 276151, 278257, 278916, 285691, 293223, 294307, 295393, 299593, 301951, 304153, 305320, 306363, 310807, 315283, 316407, 319125, 320923, 326613, 330051, 335923, 338143, 339307, 340473, 342811, 345157, 354621, 357007, 358203, 359401, 360601, 363007, 364213, 365421, 367843, 373933, 383781, 388753, 391251, 393757, 394420, 395013, 406901, 416671, 419257, 423151, 425757, 433623, 444223, 444829, 445557, 446893, 448231, 453603, 454951, 456301, 459007, 464443, 468541, 471283, 478173, 480943, 482331, 485113, 489301, 490701, 493507, 499143, 500557, 501973, 506233, 509083, 511941, 513373, 517681, 518481, 519121, 520563, 524287.

Some larger examples :